A nonlocal plate model incorporating interatomic potentials for vibrations of graphene with arbitrary edge conditions

• Explicit nonlocal frequency formulas based on interatomic potentials are derived for SLGSs with various edge supports.
• The formulas not depending on Young's modulus enable simple calibration of scale coefficient using MD results.
• The analytical expressions are shown to be capable of predicting vibrational response of SLGSs accurately.
• The prominence of size effect in frequency of SLGS is found to be dependent on side length and boundary conditions.

This article presents analytical explicit frequency expressions for investigating the vibrations of single-layer graphene sheets (SLGSs). The interatomic potential is incorporated into a nonlocal continuum plate model through establishing a linkage between the strain energy density induced in the continuum and nonlocal plate constitutive relations. The model which is independent of scattered value of Young's modulus is then applied and explicit frequency formulas for the SLGSs with different edge conditions are derived using static deflection function of the nanoplate under uniformly distributed load. The reliability of the present formulation is verified by the results obtained by the molecular dynamics (MD) simulations and other research workers. The formulas are of a simple short form enabling quick and accurate evaluation of the frequency of the SLGSs and also simple calibration of scale coefficient by the use of MD simulations results.